Anonymous wrote:> George:> >>I was taught (33 years ago in the University of Birmingham, UK) that a>>vector space is>>(1) a set of elements (the vectors) which form an abelian group under>>addition;>>(2) etc....>>The phrase "commutative group" or "additive group" might have been used>>instead of "abelian group"--you'll forgive me if I can't quite remember!>>> > I think you just made me remember what an abelian group is.> It's closed under its operation, it's associative, commutative,> it's got an inverse, and it's got the identity element in it.> There may be some other condition, since aren't> all the above needed for any group?> I remember something about an abelian group forming a table> with a diagonal, or something....

To remarks:

(1) too many "It's", referring to different things.

(2) this would be an excellent time, to grab a textbook or your notes and _lookup_ the definition of "group" and "abelian group".

> Rather than listing all 8 conditions. But, that assumes the student *knows*> what an abelian group is.

Not really. One can list all the conditions; but it would be nice at leastto group the conditions in a coherent way and to mention those conditionsthat correspond to the axioms for an abelian group.Those students who have met "abelian groups" before would benefit andthe others would not be hurt.